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MATHEMATICS FOR FINANCE
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MATHEMATICS FOR FINANCE
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Academic year 2019/2020
- Course ID
- SEM0065
- Teaching staff
- Bertrand Lods (Lecturer)
Marina Marena (Lecturer)
Elisa Luciano (Lecturer)
Alessia Nota (Lecturer) - Degree course
- Finance
Insurance and Statistics - Year
- 1st year
- Teaching period
- First semester
- Type
- Distinctive
- Credits/Recognition
- 12
- Course disciplinary sector (SSD)
- SECS-S/06 - metodi matematici dell'economia e delle scienze att. e finanz.
- Delivery
- Formal authority
- Language
- English
- Attendance
- Obligatory
- Type of examination
- Written
- Prerequisites
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A good knowledge of basic calculus (Matematica Generale), of the foundations of probability calculus and statistical infererence (Statistica)
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Sommario del corso
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Course objectives
This course is aimed at introducing and developing many of the mathematical tools which are used in applied finance and insurance. ln this module, particular stress will be posed on the development of the measure theoretical tools and advanced probability concepts with emphasis on their applications to investment and insurance decisions. The introduction of stochastic processes and their properties is always motivated by the wish to develop models for observed phenomena.- Oggetto:
Results of learning outcomes
At the end of the course, the student is expected to be capable of:- using the basic tools and results to pose, formalize and solve a probability problem of applied interest
- knowing the extent to which the results obtained in the previous step are dependent on the assumption that s/he has made about the behaviour of the economic agents
- being able to think about possible and useful generalizations of the model
- being able to communicate such findings using appropriate and clear mathematical notation and language
CONOSCENZA E CAPACITÀ DI COMPRENSIONE
Scrivi testo qui...CAPACITÀ DI APPLICARE CONOSCENZA E COMPRENSIONE
Scrivi testo qui...AUTONOMIA DI GIUDIZIO
Scrivi testo qui...ABILITÀ COMUNICATIVE
Scrivi testo qui...CAPACITÀ DI APPRENDIMENTO
Scrivi testo qui...KNOWLEDGE AND UNDERSTANDING
Write text here...APPLYING KNOWLEDGE AND UNDERSTANDING
Write text here...INDEPENDENT JUDGEMENT
Write text here...COMMUNICATION SKILLS
Write text here...LEARNING SKILLS
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Course delivery
The course is articulated in 96 hours of formal in-class lecture time, and in at least as many hours of at-home work solving practical exercises.- Oggetto:
Learning assessment methods
The course grade is determined solely on the basis of a written examination. The examination tests the student's ability to do the following:- Present briefly the main ideas, concepts and results developed in the course, also explaining intuitively the meaning and scope of the definitions and the arguments behind the validity of the results
- Use effectively the concepts and the results to answer questions in basic measure theory and stochastic process theory, e.g., computing the Ito integral of some given stochastic process.
The above is accomplished by asking the student to answer open questions: 1-3 questions on part 1 (7.5 points in total), 1-4 questions on part 2 (12.5 points in total), and 1-3 questions on part 3 (10 points in total). The points assigned to each question will be stated on the exam sheet. Questions can be essay questions or exercises.
The exam is a closed-books exam lasting 2.45 hours. Use of calculators is not permitted.
The student can take the exam at most three times per academic year on a total of five exam sessions (December, January, February, June and September).
During the Covid-19 emergency the learning assessment method will consist in a written exam with video surveillance on Webex. Students are referred to the Moodle page of the course for detailed informations.
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Support activities
Short course on "Essentials of Mathematics" held in September.- Oggetto:
Program
The course is divided into three parts:Part 1 [24 hours]: Discrete-time economies (Luciano)
- Pricing of redundant securities.
- Investor optimality and pricing in the case of homogeneous investors.
- Equilibrium and pricing of basic securities.
Part 2 [40 hours]: Measure, Probability and basics of decision making (Lods)
- Review of differential and integral calculus.
- Foundations of measure theory. Measures, measurable functions, Lebesgue integrals, Lp spaces, theorems of Fubini and Radon-Nikodym.
- Applications of measure theory to probability calculus. Conditional probabilities and expectation, filtrations.
- Martingales and their convergence.
Part 3 [32 hours] : Stochastic Processes (Marena)
- Brownian motion.
- Stochastic calculus.
- Connection with PDEs.
- Change of measure.
- Introduction to jump processes.
Suggested readings and bibliography
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The following are the required textbooks for the course:Part 1
- Dumas, B., Luciano, E. (2017). The economics of continuous-time finance. MIT Press.
Part 2
- Capinski, Kopp (2005). Measure, Integral and Probability, Second Edition, Springer-Verlag.
Part 3
- Shreve (2004). Stochastic calculus for finance II, Springer.
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Class schedule
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